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  • A ring of mass m and radius r is lying on a horizontal plane as shown in the figure. If the ratio of moment of inertia about two axes is I1 and I2 respectively. Then

A ring of mass m and radius r is lying on a horizontal plane as shown in the figure. If the ratio of moment of inertia about two axes is I1 and I2 respectively. Then find the ratio of I1 and I2.

Option: 1

\frac{1+2sin^{2}\theta _{1}}{1+2sin^{2}\theta_{2}}


Option: 2

\frac{1+2cos^{2}\theta_{1}}{1+2cos^{2}\theta_{2}}


Option: 3

\frac{1+2sin^{2}\theta_{1}}{1+2cos^{2}\theta_{2}}


Option: 4

\frac{1+2cos^{2}\theta_{1}}{1+2sin^{2}\theta_{2}}


Answers (1)

best_answer

I_{1}=I_{c.m}+m(rsin\theta_{1})^{2}\\I_{1}=\frac{mr^{2}}{2}+mr^{2}sin^{2}\theta_{1}=\frac{mr^{2}}{2}[1+2sin^{2}\theta_{1}]\\ I_{2}=I_{c.m}+m[rsin\theta_{2}]^{2}\\I_{2}=\frac{mr^{2}}{2}[1+2sin^{2}\theta_{2}]\\\frac{I_{1}}{I_{2}}=\frac{1+2sin^{2}\theta_{1}}{1+2sin^{2}\theta_{2}}

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Gaurav

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